Q51.The number of real roots of the equation, e4x + e3x −4e2x + ex + 1 = 0 is: (1) 1 (2) 3 (3) 2 (4) 4
What This Question Tests
This question tests the ability to transform an exponential equation into a polynomial equation using substitution and then determine the number of positive real roots for the transformed variable.
Concepts Tested
📚 NCERT Sections This Tests
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
3.26 — The Decomposition Of Hydrocarbon Follows The Equation
Chemistry Class 11 · Chapter 3
3.26 The decomposition of hydrocarbon follows the equation k = (4.5 × 1011s–1) e-28000K/T Calculate Ea. 87 Chemical Kinetics Reprint 2025-26
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of exponential equations
- Year
- 2020
- Shift
- 09 Jan Shift 1
- Q Number
- Q51
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations; Class 12 Mathematics Ch 5: Continuity and Differentiability
More from this Chapter
Q83.If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5, then the set of possible values of a is JEE Main 2007 JEE Main Previous Year Paper (1) (−3, 3) (2) (−3, ∞) (3) (3, ∞) (4) (−∞, −3)
Q72.The quadratic equations x2 −6x + a = 0 and x2 −cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is (1) 1 (2) 4 (3) 3 (4) 2
Q61.If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is (1) greater than 4ab (2) less than 4ab (3) greater than −4ab (4) less than - 4ab
Q61.The value of k for which the equation (K −2)x2 + 8x + K + 4 = 0 has both roots real, distinct and negative is (1) 6 (2) 3 (3) 4 (4) 1